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Find the greatest number that will divide 446, 573, and 700 leaving the remainders 5, 6, and 7 respectively.
Given: A number would divide 446, 573 And 700 and leave remainders 5, 6, and 7 respectively.
To find: We have to find that greatest number.
Solution:
If that number divide 446, 573, 700 leaving remainder 5, 6, 7 respectively, this means that number will divide 441(446 - 5), 567(573 - 6) and 693(700 - 7) completely.
Now, we just have to find the HCF of 441, 567 and 693.
HCF of 441, 567 and 693:
Factors of 441 = 3 x 3 x 7 x 7
Factors of 567 = 3 x 3 x 3 x 3 x 7
Factors of 693 = 3 x 3 x 7 x 11
Now the highest common factor is = 3 x 3 x 7 = 63.
So the largest number that will divide 446, 573, 700 leaving remainder 5, 6, 7 respectively is 63.
Updated on: 10-Oct-2022
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